African swine fever is a devastating disease that can result in death in almost all infected pigs. The continuing spread of African swine fever from Africa to Europe and recently to the high-pig production countries of China and others in Southeast Asia threatens global pork production and food security. The African swine fever virus is an unusual complex DNA virus and is not related to other viruses. This has presented challenges for vaccine development, and currently none is available. The virus is extremely well adapted to replicate in its hosts in the sylvatic cycle in East and South Africa. Its spread to other regions, with different wildlife hosts, climatic conditions, and pig production systems, has revealed unexpected epidemiological scenarios and different challenges for control. Here we review the epidemiology of African swine fever in these different scenarios and methods used for control. We also discuss progress toward vaccine development and research priorities to better understand this complex disease and improve control.